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Remasking allows diffusion language models to revisit generated text, but effective correction requires knowing when and what to revise. Our diagnosis on Sudoku reveals two gaps. Hidden states contain error information that token confidence does not reliably expose, and remasking an isolated error usually reproduces it when the surrounding context remains fixed. These findings motivate DiVR , a verifier that predicts whether a partially generated sequence will reach a correct answer. Trained on the final correctness of the model's own trajectories, DiVR decides when to regenerate a block and which alternative to retain, while the generator itself stays unchanged. On five reasoning benchmarks with LLaDA-8B-Base, DiVR raises the average accuracy of the fine-tuned generator from 35.3\% to 43.4\% at $1.9$-$3.5\times$ the cost of greedy decoding, above search baselines that use $3.8$-$7.4\times$. It also complements post-training such as supervised fine-tuning and reinforcement learning, and generalizes to other generators, including Dream.

Debate has been recently proposed as a training protocol that is hoped to produce more aligned models even as model capabilities scale. The idea is that the human, instead of providing supervision in the form of labels, judges a debate between two models that compete to prove the correctness of opposite labels. It can be shown that functions of a much higher computational complexity can be correctly judged in this way, compared to the complexity of functions that can be directly evaluated using a computationally weak evaluator. This suggests that perhaps debate can be used to teach very complicated functions to models. However, previous work has largely ignored the fact that this is a training protocol, and simply analyzes the game being played between the two debaters for a known judge. We take the first steps towards understanding the learning problem implicit within the protocol, by formulating it as an online learning problem. We show that once we formulate the learning problem precisely, there are cases where the best way to learn given access to a judge is different from running an adversarial debate. This motivates us to define a cooperative version of the protocol, whose learnability we characterize using a combinatorial dimension. We also consider the possibility of the human judge being fallible and occasionally judging the debate incorrectly. We show that a small number of errors in judgement can lead to a large error in learning.

Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise ($\varepsilon$) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional settings. However, a formal explanation of why the optimal target depends on the specific properties of the data remains elusive. In this work, we provide a theoretical framework based on a generalized prediction formulation $u=kx-(1-k)n$, where $x$ represents clean data and $n$ denotes noise. This formulation accommodates arbitrary targets, of which $\varepsilon$-, v-, and x-prediction are special cases. We derive the analytical relationship between data's geometry and the optimal prediction target, offering a rigorous justification for why x-prediction becomes superior when the ambient dimension significantly exceeds the data's intrinsic dimension. Furthermore, our controlled analysis reveals how time conditioning and loss variations systematically modulate this optimal objective. While our theory identifies dimensionality as the governing factor for the optimal prediction target, the intrinsic dimension of manifold-bound data is typically intractable to estimate in practice. To bridge this gap, we propose k-Diff, a framework that employs a data-driven approach to learn the optimal prediction parameter k directly from data, bypassing the need for explicit dimension estimation. Extensive experiments in both latent-space and pixel-space image generation demonstrate that k-Diff consistently outperforms fixed-target baselines across varying architectures and data scales, providing a principled and automated approach to enhancing generative performance.

On-device inference requires kernels that make effective use of local accelerators. Efficient training and evaluation of models that generate Apple Metal kernels benefit from native macOS tools and concurrent agent sessions. These sessions alternate between model requests, development commands, and GPU execution, leaving GPU capacity idle for much of a rollout. We present Metal Sandbox, infrastructure that combines restricted per-instance file access, native command execution, and command-level scheduling across interconnected Macs. Each agent retains its workspace and private development environment. Parallel commands can run concurrently, while serial commands share one execution slot per node; eligible waiting commands can migrate to available Macs and return results to the original agent. Integration with Harbor supports task execution, automatic verification, and rollout collection through a common workflow. Controlled experiments on four Mac mini M4 nodes achieve $1.68\times$--$2.05\times$ gains in command throughput under concentrated demand. Sixteen static agent traces give an estimated $2.14\times$ sustained-throughput gain for four sessions per node versus one, assuming continuously replenished sessions and unchanged mean durations. Replaying these measured traces under dynamic scheduling reduces mean tool waiting by 18.8% and batch elapsed time by 22.3%, assuming unchanged phase durations. Metal Sandbox and its Harbor integration are open-source on GitHub.

Despite the success of discrete diffusion language models (dLMs) for fast parallel decoding, their non-smooth, high-dimensional space hinders trajectory steering for reasoning and inference acceleration. To overcome this, we present Nemotron-Labs-Sigma, the first family of large-scale (3B/8B) continuous dLMs built on steerable, low-dimensional ODE/SDE latent trajectories. Trained blockwise via likelihood optimization, Nemotron-Labs-Sigma jointly denoises Gaussian-corrupted token embeddings while learning an optimal embedding geometry, and leverages pretrained autoregressive (AR) weights for warm-starting. At inference, we identify classifier-free guidance and score temperature as essential for high-fidelity reasoning and coding. Against state-of-the-art discrete counterparts (masked dLMs and AR baselines), Nemotron-Labs-Sigma outperforms them on standard benchmarks after pretraining (e.g., GSM8K, Minerva, HumanEval, MBPP) and on challenging reasoning tasks after supervised fine-tuning (e.g., MATH-500, AIME), with the largest consistent gains on coding. Beyond accuracy, we exploit two structural properties unique to continuous dLMs. First, smooth trajectories degrade gracefully at low NFEs and enable efficient few-step distillation: distribution matching proves strongest among the methods we study, giving roughly 8x acceleration on math and 4x on coding (8 and 4 tokens per forward pass) with negligible accuracy loss and preserved diversity. In addition, the one-step speculative decoding on the (pre-SFT) distilled 8B model yields a further ~3.5x throughput gain over the AR counterpart (on GB200), outperforming masked dLM baselines. Second, embedding-space steering controls the quality--diversity trade-off, yielding strong pass@$k$ that keeps improving as $k$ grows. Together, these results establish continuous dLMs as a promising paradigm for efficient language generation.

The use of Large Language Models (LLMs) to simulate social actors has garnered attention for its implications for the epistemic status of discourses generated through such means. This paper considers the more modest question of whether sociological role-playing can serve as a heuristic instrument in the generation of qualitative hypotheses. We take as a case study the development of four divergent fictional characters using a theoretically informed Matrix of Climate Reception. These characters are asked to respond to a series of discourse frames covering two topics: a proposed ban on the sale of new gasoline-powered cars, and the inclusion of climate justice in the school curriculum. We then analyse the 32 model-generated responses for their commonalities, situational differences and divergences from the presuppositions underlying the characters' profiles. The experiment illustrates how LLMs can be used to flesh out theoretical presuppositions into contextual narratives and to propose avenues of further inquiry. It also shows that role-playing can generate considerable similarity between characters and is sensitive to how prompts are constructed, warning against the confusion of discursive coherence with sociological data. Role-playing is argued to be just one of several possible ways to use LLMs for generating hypotheses, with the heuristic specificity of this procedure compared with other methods of direct LLM-based reasoning or with other techniques remaining an open issue. The qualitative laboratory is thus conceived of as a heuristic instrument for provoking reflection and refining questions, not for testing theories with artificial data.